23.6.4 problem 4

Internal problem ID [6803]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 6. THE EQUATION IS NONLINEAR AND OF ORDER GREATER THAN TWO, page 427
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 03:51:51 PM
CAS classification : [[_3rd_order, _exact, _nonlinear]]

\begin{align*} y^{2}-\left (1-2 x y\right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=f \left (x \right ) \end{align*}

✗ Maple

ode:=y(x)^2-(1-2*x*y(x))*diff(y(x),x)+x*diff(diff(y(x),x),x)+x^2*diff(diff(diff(y(x),x),x),x) = f(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]^2 - (1 - 2*x*y[x])*D[y[x],x] + x*D[y[x],{x,2}] + x^2*D[y[x],{x,3}] == f[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 3)) + x*Derivative(y(x), (x, 2)) - (-2*x*y(x) + 1)*Derivative(y(x), x) - f(x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2*Derivative(y(x), (x, 3)) - x*Deriva